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Intuition as explained here is totally rational but arrived at by an unconscious process of synthesizing a body of knowledge rather than by a conscious step by step approach
Thus a poseik who has mastered the classic texts can make a leap of logic without necessarily being able to articulate the steps needed to arrive at his conclusion.
I have seen intuition unfairly rejected as "supernatural" lo bashamayim heed. Intuition is usually just the case of a master in his field taking it all in in the vast subconscious mind without being able to break it down.Lemashal, a baseball hitter is factoring in all kinds off training and experience when facing a major league pitcher who can throw a 90+ Mph fastball vs. A 75 Mph change-up etc. The vast number of steps in experience and muscle memory are perhaps too complex to explain. But years of training and experience can make a master hitter without consciously knowing the minutia.Ideally teachers need to share their thinking process in order to train others. But sometimes Master Poskim have an intuitive knowing that transcends a step-by-step approach but is also not "supernatural" but rather a gestalt as a result of mastering vast tracts of material.